Reuleaux triangle confusion (I'm trying to measure a tabletop insert to replace the glass that broke.)

T

titanium

New member
Joined
Jul 26, 2023
Messages
3
Hello, I'm stumped by a seemingly simple situation. I'm trying to measure a tabletop insert to replace the glass that broke. I thought it was a regular Reuleaux triangle, but it's not. The diameter [apex to opposite arc midpoint] is shorter than the chord [leg of inner triangle]. I measured the arc length, but how do I figure out the size of the circle which includes it? If it were a standard Reuleaux, it would be a 60 deg arc, but since the chord is not the circle radius, I don't know how to determine the arc in degrees, nor the actual radius. Help me, Obi Wan Kenobi!
 
titanium said:
Hello, I'm stumped by a seemingly simple situation. I'm trying to measure a tabletop insert to replace the glass that broke. I thought it was a regular Reuleaux triangle, but it's not. The diameter [apex to opposite arc midpoint] is shorter than the chord [leg of inner triangle]. I measured the arc length, but how do I figure out the size of the circle which includes it? If it were a standard Reuleaux, it would be a 60 deg arc, but since the chord is not the circle radius, I don't know how to determine the arc in degrees, nor the actual radius. Help me, Obi Wan Kenobi!
Click to expand...
Can you attach an image of the tabletop, so we can be sure of the configuration?

One way to determine the radius of an arc is shown here:

Radius of an Arc or Arch with calculator - Math Open Reference

www.mathopenref.com
 
titanium said:
Hello, I'm stumped by a seemingly simple situation. I'm trying to measure a tabletop insert to replace the glass that broke. I thought it was a regular Reuleaux triangle, but it's not. The diameter [apex to opposite arc midpoint] is shorter than the chord [leg of inner triangle]. I measured the arc length, but how do I figure out the size of the circle which includes it? If it were a standard Reuleaux, it would be a 60 deg arc, but since the chord is not the circle radius, I don't know how to determine the arc in degrees, nor the actual radius. Help me, Obi Wan Kenobi!
Click to expand...
First of all, it's not obvious to me that the curved sides are arcs. Here's how I would confirm that they are and find the radius.
Pick 2 points on one of the sides. Put a ruler next to one of the points so that it forms a tangent line. Put another ruler/straight line through the same point at 90 degrees to the first ruler. Draw a line along the second ruler. Repeat for the second point. If the curve is circular the 2 lines intersect at the circle's center. The distance from the center to any of the points is the radius. But you need to confirm that all points of the curve lie at that same distance from the center.
One potential problem is that the 2 tangent lines would not be exact. Try picking more points to improve accuracy.
 
lev888 said:
First of all, it's not obvious to me that the curved sides are arcs. Here's how I would confirm that they are and find the radius.
Pick 2 points on one of the sides. Put a ruler next to one of the points so that it forms a tangent line. Put another ruler/straight line through the same point at 90 degrees to the first ruler. Draw a line along the second ruler. Repeat for the second point. If the curve is circular the 2 lines intersect at the circle's center. The distance from the center to any of the points is the radius. But you need to confirm that all points of the curve lie at that same distance from the center.
One potential problem is that the 2 tangent lines would not be exact. Try picking more points to improve accuracy.
Click to expand...
I just solved it with this fancy arc calculator:

The Complete Circular Arc Calculator

www.handymath.com

But thanks for taking the time to respond!
 
You must log in or register to reply here.
Top